Problem Solving and the Ontario Curriculum
The set of skills our children need today extends beyond the traditional paper and pencil calculation
skills that dominated mathematics instruction that most parents remember. In addition to having a good
understanding of number facts and the ability to work with numbers, there are other important skills
such as reasoning, problem solving and the communication of mathematical ideas that are also essential
in the twenty-first century. For example, students need experience with making estimates, deciding on
and adjusting their strategies, persevering through to a solution, and justifying their thinking. The
Ontario Curriculum; Mathematics, Grades 1-8 (2005) supports the development of this mathematical
thinking in a way that is meaningful and relevant to students.
You can help your child to become a confident math problem solver by demonstrating persistence and a
willingness to try multiple strategies or ideas. Also, talking through these challenges will help your child
to develop his/her ability to improve communication skills and the development of math vocabulary. Be
sure to encourage the use of concrete materials (e.g., coins, counters, shapes) as well as visuals (e.g.,
making a chart, drawing a diagram) when working through these math tasks.
There are five strands in the Ontario Curriculum:
Number Sense and Numeration
Geometry
Data Management and Probability
Measurement
Patterning and Algebra
In addition, there are 7 Mathematical Process Expectations which permeate the curriculum:
Problem Solving
Reasoning and Proving
Reflecting
Selecting Tools and Computational Strategies
Connecting
Representing
Communicating
For more information on the Ontario Mathematics Curriculum visit:
http://www.edu.gov.on.ca/eng/curriculum/elementary/math18curr.pdf
The challenge for this week is focused on skills found within the Number Sense and Numeration Strand
and addresses several grade level expectations including:
Grade Seven:
 Represent, compare, and order decimals to hundredths and fractions, using a variety of tools
 Add and subtract fractions with simple like and unlike denominators
Grade Eight:
 Solve problems involving addition, subtraction, multiplication and division of fractions
 Solve problems involving proportions, using concrete materials, drawings and variables
This challenge is appropriate for both grade seven and eight, and addresses important mathematical
ideas related to fractions and proportional reasoning.
This flag was designed with four main colours – orange, blue, yellow and green.
Determine the fraction of the flag that is:
C
What fraction of the flag is not green? Explain your reasoning?
How much more of the flag is orange than blue? Show how you found the difference.
Create your own flag challenge and see if a friend or family member can determine the
answer.
Think about:
How can I use my understanding of 2D shapes to help make comparisons?
Is there more than one way to find the answers?
Encourage your child to use proportional reasoning to explain the relationships
between the colour squares. For example, “I can see that the smaller square which is
divided into four triangles is the same area as the one of the long rectangles. Both areas
show one-fourth of the whole”.
Challenge # Two
Create your own flag using the same colours as used in the flag above. You must
divide your flag into at least 8 sections and use only straight lines. What fraction of
the flag is covered by each colour?
http://www.edugains.ca/resources/LearningMaterials/TIPS/tips4rm/grade7/Unit7_
FractionsDecimals.pdf